Elsevier

Surface Science

Volume 696, June 2020, 121594
Surface Science

Molecular dynamics simulations of the growth of Ge on Si

https://doi.org/10.1016/j.susc.2020.121594Get rights and content

Highlights

  • MD simulations of Ge island formation on Si.

  • Mixed Si–Ge dimers can form growing into mixed wetting layers.

  • Diffusion pathways identified by MD and NEB.

  • Square based island structures form.

  • Ge atoms can diffuse onto islands through multiatom rearrangements.

Abstract

The initial stages of the growth of germanium on the dimer reconstructed Si(100) surface is modelled using molecular dynamics (MD). Pyramidal island structures are observed to form despite MD being carried out at a deposition rate faster than experiment. By an examination of transitions that can occur from intermediate structures that form in the MD simulations, growth mechanisms can be identified. The initial wetting occurs as a result of Ge atoms diffusing into the trenches between the dimer rows. This results in Ge–Ge or Ge–Si dimer chains growing in rows perpendicular to the original Si–Si dimer rows on the surface. It is shown how strained Ge pyramids with square bases can form by diffusing atoms joining together adjacent dimer rows. From these initial square-based structures, complex concerted motions are observed in which atoms in lower layers ‘climb up’ to higher layers. Similar structures grown in the pure Si case exhibit much higher energies barriers for the ‘climbing up’ process indicating that the effect of strain is to reduce the energy barriers for pyramid formation. In addition to the investigation of atomistic growth processes, surface energy effects are also examined, which show that a germanium-covered Si(100) surface containing shallow-angled pyramids is energetically more favourable than that grown as a flat monolayer.

Introduction

Experiments reporting the growth of quantum dots of germanium on silicon first appeared in the literature 30 years ago [1], [2]. Originally, hut structures with square (pyramids) and rectangular (wedges) bases were observed and since then both pyramids and wedges have been seen dependent on the precise growth conditions [3], [4]. Due to a lattice mismatch of about 4.2% in the Ge/Si system, the Stranski-Krastanow growth mode is realised [5], [6], [7], [8]. Experiments indicate that the nucleation of large 3D clusters only occurs after the deposition of a wetting layer (WL) with a critical thickness of typically, 3–5 monolayers [9], [10].

There have been numerous experimental and theoretical studies over the years aiming to understand the precise mechanisms for the formation of the growth structures which continue to this day. A good overview of experimental work up to 2013 is given in [11]. Over a number of years heterostructures with quantum dots have been actively used for the creation of photodetectors, solar cells and light emitting devices [12], [13]. They have also found application in emerging fast-speed transistors where the engineered strain induces very high mobilities of the charge carriers [14].

Theoretical models can be broadly categorised in terms of (1) free energy models [15] (2) Kinetic Monte-Carlo (KMC) models [16], [17] (3) Quantum mechanical (Density Functional Theory, DFT) models. Whereas the DFT models can give relatively accurate values for the energies and stresses of the Ge ‘hut’ islands [18], [19] they are too expensive be used in dynamical growth simulations. The KMC models can predict the growth of pyramids with the observed (105) facets by both including the effect of strain and by artificially forcing cells that lie locally on such a face to be less mobile than other cells [16].

Larger scale free energy models have also been used to explain the growth process such as the effect of the edge energy [20], the transition from two dimensional to three dimensional growth [21], the influence of the wetting layer [22] and the role of elastic interactions between islands [23], [24]. Moreover, such models have been successfully used to describe Volmer-Weber growth of islands directly on the surface of the substrate in highly-mismatched systems [25], [26], as well as the formation of 2D layers according to Frank-van der Merwe mechanisms in systems with close lattice parameters [27], [28]. However, precise information about surface diffusion coefficients [29] and thickness-dependent surface energies [18], [19] is required for constructing these models. These are still less well-defined input parameters [30], because direct experimental measurements of these values are impossible. Despite the large amount of theoretical work which we only touch upon briefly in this introduction, there are still gaps in the theory that make direct prediction of experimental results quite difficult.

One type of model that to our knowledge has not been fully explored is the use of molecular dynamics (MD). MD is generally not so suitable for atomistic growth modelling because it cannot capture experimental growth rates. This is because time scales accessible by MD are usually of the order of microseconds at most and so diffusion between successive particle impacts is generally not so well captured. This has led to other methods such as temperature accelerated dynamics (TAD) [31] and adaptive KMC [32]. In the case of Ge growth on Si, the adaptive KMC is difficult to implement because the dimer reconstruction enlarges the search volumes in which transitions are located, making it too computationally expensive to find a representative set of transitions. However recent work [33] has shown that in certain circumstance MD at elevated temperature can be a useful tool in modelling growth on surfaces and indeed more than 30 years ago MD at elevated temperature was used on quite small systems to show how the first layer of growth of Si on the dimer reconstructed Si(100) surface occurred [34]. Another potential drawback of MD using classical potentials is that it cannot capture all the electronic details of chemical interactions. Generally ab initio methods give a better representative model; for example in the case of the dimer reconstructed Si(100) surface, ab initio methods can capture the dimer tilting observed experimentally whereas classical potentials do not. However due to the computations involved ab initio methods are impractical for growth simulations and it is expected that because a key feature of the pyramidal growth is the lattice size mismatch between Si and Ge, which the classical potentials are fitted to, MD should be able to shed some light on the growth mechanisms on the atomic scale.

Computing power has significantly increased since that initial work of Si growth on Si [34] allowing for larger systems to be investigated but the problem of enhanced deposition rates compared to experiment still exists. Notwithstanding that, elevated temperature MD can be a powerful tool for analysing complex transitions that occur in atomistic growth. This is the approach adopted here, combined with an analysis of some specific transitions which can form the explanation for how the pyramidal structures grow.

Section snippets

Methodology

Depositions were modelled via MD using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [35] package. The Tersoff potential [36] for Si–Ge was used for simulations. The potential energy surface for the system is quite rough with a combination of both very small energy barriers where the atoms change position only over a distance of fractions of an Å and larger barriers where hops are quite rare. This makes the speed-up of both TAD and adaptive KMC quite marginal. In

Simulations using a ten layer Si substrate with an area 8.7 nm  ×  8.7 nm and a Ge deposition every 0.1 ns

Before discussing individual diffusion pathways and mechanisms we first present the results from the fast deposition of about 10 added Ge layers under the conditions as described above. The results are shown in Fig. 1 after the deposition of 400 Ge atoms in Fig. 2 after 2174 atoms.

Fig. 1 shows clearly dimer rows of Ge and mixed Ge–Si atoms perpendicular to the original Si–Si dimer rows together with some regions where clustering has started to occur. The Si–Ge dimers have a spacing between 2.42

Mechanisms in the first added layer

Growth occurs by Ge atoms diffusing over the surface to two favoured sites. These sites are where the Ge atom attaches to an Si dimer or resides in the trench between adjacent dimers, pulling the adjacent Si atoms towards it. Fig. 5a shows a typical diffusion path seen in MD with the associated energy barriers determined by the nudged elastic band (NEB) method shown in 5 b. The final state is the equilibrium structure in the trench between dimer rows and the intermediate structure with the

Discussion

For many simple crystalline systems, whether island growth or layer by layer growth occurs can be roughly estimated from the Ehrlich-Schwoebel (E-S) barriers, i.e. the energy barrier for an adatom to climb up or drop off a step edge. See for example [46]. The Si(100) surface and the subsequent islands that form have complex structures with the simulations showing that addition of atoms to islands occurs by various multi-atom movements, so the concept of an E-S barrier involving single atom

Conclusion

Although the MD methodology used is too fast to capture all the diffusion processes that would occur experimentally between successive particle impacts, it gives a qualitatively accurate description of how deposited Ge atoms can develop into pyramidal structures as observed experimentally. Moreover, diffusion pathways and their associated energy barriers identified from MD calculations were used in NEB calculations to determine activation energies. The results have shown that the growth

Declaration of Competing Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

CRediT authorship contribution statement

Ying Zhou: Conceptualization, Methodology, Validation, Software, Formal analysis, Investigation, Data curation, Writing - original draft, Visualization. Adam Lloyd: Conceptualization, Methodology, Validation, Software, Investigation. Roger Smith: Conceptualization, Methodology, Validation, Software, Formal analysis, Writing - original draft, Writing - review & editing, Visualization, Supervision, Project administration, Funding acquisition. Kirill A. Lozovoy: Conceptualization, Methodology,

Acknowledgements

The authors would like to thank the Royal Society of London for an international exchange grant between Loughborough University and Tomsk State University.

References (49)

  • Y.Y. Hervieu et al.

    Kinetics of second layer nucleation with permeable steps

    Surf. Sci.

    (2014)
  • S.N. Filimonov et al.

    Step permeability effect and interlayer mass-transport in the Ge/Si(111) MBE

    Mater. Sci. Semicond. Process.

    (2005)
  • Y. Mo et al.

    Kinetic pathway in Stranski-Krastanov growth of Ge on Si(001)

    Phys. Rev. Lett.

    (1990)
  • D.J. Eaglesham et al.

    Dislocation-free Stranski-Krastanow growth of Ge on Si(100)

    Phys. Rev. Lett.

    (1990)
  • L.V. Arapkina et al.

    Nucleation of Ge quantum dots on the Si(001) surface

    Phys. Rev. B

    (2010)
  • C. Priester et al.

    Origin of self-assembled quantum dots in highly mismatched heteroepitaxy

    Phys. Rev. Lett.

    (1995)
  • O.P. Pchelyakov et al.

    Silicon-germanium nanostructures with quantum dots: formation mechanisms and electrical properties

    Semiconductors

    (2000)
  • J. Wu et al.

    Quantum dot optoelectronic devices: lasers, photodetectors and solar cells

    J. Phys. D

    (2015)
  • T. David et al.

    New strategies for producing defect free SiGe strained nanolayers

    Sci. Rep.

    (2018)
  • V.G. Dubrovskii et al.

    Kinetics of the initial stage of coherent island formation in heteroepitaxial systems

    Phys. Rev. B

    (2003)
  • P. Gaillard et al.

    Kinetic Monte-Carlo simulations of the growth of silicon germanium pyramids

    Phys. Rev. B

    (2013)
  • S.N. Filimonov et al.

    Kinetics of two-dimensional island nucleation on reconstructed surfaces

    Phys. Rev. B

    (2012)
  • G.H. Lu et al.

    Towards quantitative understanding of formation and stability of Ge hut islands on Si(001)

    Phys. Rev. Lett.

    (2005)
  • G.H. Lu et al.

    First-principles study of strain stabilization of Ge(105) facet on Si(001)

    Phys. Rev. B

    (2005)
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